This is not a correct description of past climate changes. The glacial and interglacial periods of the last 2.5 million years have been global and swinging temperatures by 6-9°C in either direction, with periods between 40-100k years.
During the last interglacial (Eemian, ca. 129–116k years ago) sea level was 6-9 meters higher than today; Scandinavia was an island. The water temperature of the North Sea was about 2°C higher than at present; hippos lived as far North as the Rhine and the Thames. The onset of the Eemian took just a few centuries, during which global temperatures shot up >5°C.